Matrices related to Dirichlet series

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dc.creatorCardon, David A.
dc.date2008-08-30
dc.date.accessioned2026-07-07T09:59:38Z
dc.date.available2026-07-07T09:59:38Z
dc.descriptionWe attach a certain $n \times n$ matrix $A_n$ to the Dirichlet series $L(s)=\sum_{k=1}^{\infty}a_k k^{-s}$. We study the determinant, characteristic polynomial, eigenvalues, and eigenvectors of these matrices. The determinant of $A_n$ can be understood as a weighted sum of the first $n$ coefficients of the Dirichlet series $L(s)^{-1}$. We give an interpretation of the partial sum of a Dirichlet series as a product of eigenvalues. In a special case, the determinant of $A_n$ is the sum of the Möbius function. We disprove a conjecture of Barrett and Jarvis regarding the eigenvalues of $A_n$.
dc.description17 pages
dc.identifierhttps://arxiv.org/abs/0809.0076
dc.identifierhttp://arxiv.org/abs/0809.0076
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/168093
dc.subjectNumber Theory
dc.titleMatrices related to Dirichlet series
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